The properties of the Higgs boson under the pure \({\cal CP}\) -even hypothesis and its coupling to top quarks are studied by ATLAS and CMS in great detail. An overview of early LHC Run 2 results on the constraints on the \({\cal CP}\) -even top-Yukawa coupling \(y_t\)  can be found in Refs. [1]}, [2]}. Early fits to a possible \({\cal CP}\)  admixture to the observed Higgs state have been performed using Run 1 and partially early Run 2 data, either investigating all Higgs-boson couplings [3]}, [4]}, or focusing on the Higgs–top-quark interaction [5]}, [6]}. These analyses could set only very weak bounds on possible \({\cal CP}\)  violation in the Higgs-boson sector. Projections for future bounds on possible \({\cal CP}\) -admixtures of the discovered Higgs-boson based on \(gg \rightarrow H + 2\)  jets data were obtained in Ref. [7]}, [8]}, [9]}, focusing on current and future Run 3 data. Experimental bounds on the top-Yukawa coupling under the \({\cal CP}\) -even coupling assumption have been obtained more recently using an integrated luminosity of \(36 \,\, \mathrm {fb}^{-1}\)  in the \(t \bar{t}\, t \bar{t}\)  channel [10]} and \(t \bar{t}\)  kinematic distributions [11]}.
